Liquid-Nitrogen Micropillar-Wick Cooling for Cryogenic Electronics: A Numerical Study of Thermal Performance and Capillary Dry-Out Limits

Abstract: Cryogenic computing technologies are maturing rapidly, but heat removal remains a key challenge when increasing the device density and operating power. Two-phase evaporative cooling is a promising approach to solve this issue, because it can dissipate high heat fluxes while maintaining small temperature rises. Here, we numerically investigate liquid-$\mathrm{N_2}$-filled silicon micropillar wicks as a capillary-fed thin-film evaporation concept for cryogenic electronics. The model combines Young-Laplace meniscus calculations, Hertz-Knudsen-Schrage evaporation, unit-cell heat-transfer and liquid-flow simulations, and an array-level thermal and capillary-flow model. For a representative geometry with a pillar diameter of $10\,μ\mathrm{m}$, pitch of $24\,μ\mathrm{m}$, and pillar height of $75\,μ\mathrm{m}$ at an applied heat flux of $20\,\mathrm{W\,cm<sup>{-2}}$, the predicted chip-temperature rise is approximately $2.7\,\mathrm{K}$. This is substantially below the estimated temperature rises for representative conduction cooling through an indium-interlayered copper heat sink and direct liquid-$\mathrm{N_2}$ immersion. The corresponding predicted single-fed dry-out length is approximately $2.7\,\mathrm{mm}$, equivalent to an ideal double-fed coolable width of approximately $5.3\,\mathrm{mm}$. The results indicate that local thermal performance is favorable, whereas lateral scalability is primarily constrained by capillary dry-out. An approximate capillary-viscous scaling relation provides a compact framework for comparing dry-out limits across working fluids and related wick geometries and for identifying strategies to extend capillary-fed transport.